Zhang [1]} gave the definition of the projection body for a compact set with piecewise \(C^1\) . Similarly, for \(K\in \mathcal {S}_o^n\cap \mathcal {C}^n\) , we define the Orlicz projection body \(\Pi _{\phi }K\) of \(K\)  as
\(h_{\Pi _{\phi }K}(u)=\inf \left\lbrace \lambda >0:\int _{\partial ^{\ast } K}\phi \left(\frac{u\cdot v_K(y)}{\lambda y\cdot v_K(y)}\right)y\cdot v_K(y)d\mathcal {H}^{n-1}(y)\le n|K|\right\rbrace .\) 
